Question: Ashley is 6 years older than Christopher. For the last 3 years, Ashley and Christopher have been going to the same school. Nine years ago, Ashley was 4 times as old as Christopher. How old is Ashley now?
Explanation: We can use the given information to write down two equations that describe the ages of Ashley and Christopher. Let Ashley's current age be $a$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $a = c + 6$ Nine years ago, Ashley was $a - 9$ years old, and Christopher was $c - 9$ years old. The information in the second sentence can be expressed in the following equation: $a - 9 = 4(c - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$ , we get: $c = a - 6$ . Substituting this into our second equation, we get the equation: $a - 9 = 4($ $(a - 6)$ $ -$ $ 9)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 9 = 4a - 60$ Solving for $a$ , we get: $3 a = 51$ $a = 17$.